Simon Says
Of course as we all know, each Die Hard film originally began life as an entirely different story. For Die Hard, it was the 1979 novel Nothing Lasts Forever, which was a sequel to The Detective. It was also said to had almost been made as a Commando sequel with Arnold Schwarzenegger, but Arnie backed out and it was reworked into a standalone film.
But how about Die Hard with a Vengeance, which originally began life as a standalone script titled Simon Says by Jonathan Hensleigh. It's been said that it almost became an action vehicle for Brandon Lee, whether a standalone film or a Rapid Fire sequel. Then it was said to had been almost considered as the basis for Lethal Weapon 4 by producer Joel Silver.
Hensleigh said that the first hour of DHwaV is literally based on his original Simon Says script, with minor differences. Of course, the main protagonist was also a New York cop; but Zeus was originally a female, leading to a romantic relationship with the NY cop. His script was incomplete, so the film's second-half was written specifically for the film to make it more Die Hard.